I know there are debates about whether the error exists and its distribution in the case of logistic regression.

Suppose we assume that the error term follows the logistic distribution. Are we looking for a set of betas that will make the error term generated accordingly (in the population) satisfy the logistic distribution using maximum likelihood?

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    $\begingroup$ I think this question is too vague to answer. You can't expect an entire chapter on logistic regression as the answer. Please focus down on exactly what your question is. $\endgroup$ Jan 13, 2020 at 1:11
  • $\begingroup$ question modified. Thank you! $\endgroup$
    – Yuan
    Jan 13, 2020 at 18:38
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    $\begingroup$ Your question is predicated on a mischaracterization. Maximum Likelihood does not find parameters that make the errors look like they conform to a particular distribution. By definition, it finds parameters that maximize the likelihood of the sample. In many (perhaps most) cases, some of the data simply don't fit in with the others and (therefore) there is no combination of parameter values that will make all the data conform to a preconceived distributional form. $\endgroup$
    – whuber
    Jan 13, 2020 at 18:49
  • $\begingroup$ So we do assume that in the population, there is a set of betas that will make the error term generated accordingly to satisfy the logistic distribution. But the maximum likelihood doesn't aim to estimate that set of beta. Is that correct? If so, how can we conduct hypothesis testing based on beta we got through maximum likelihood? Thank you $\endgroup$
    – Yuan
    Jan 13, 2020 at 20:47